Disappointingly Average

Subotnik et al generally seem to hold what has been called the ‘resource’ model of gifted education: high IQ children have much better odds of growing up into the great movers & shakers and thinkers of the world who have disproportionate influence on what happens (definitely); that special measures such as enriched education, schools with peers in intelligence, and accelerated courses will increase the yield of great (maybe); and that the increase justifies the upfront expenses (uncertain).

By success, they have high standards; Gallagher’s foreword speaks for the rest of the book when it says:

The authors were disappointed to discover that although this sample succeeded admirably in traditional terms, with its share of physicians, lawyers, and professors, there were no creative rebels to shake society out of its complacency or revolutionize a field.

Further:

Norbert Wiener, in his book The Autobiography of an Ex-Genius [actually, Ex-Prodigy: My Childhood and Youth & I Am Mathematician], detailed his unhappy family life with a domineering father and enough personal problems to be in and out of mental institutions. Yet, it was this Norbert Wiener who gave the world cybernetics that revolutionized our society. What if he had had a happy family life with a warm and agreeable father? One is left to wonder whether Wiener would have had the drive and motivation to make this unique contribution. The same question can be posed for these Hunter College Elementary School graduates. Are many of them too satisfied, too willing to accept the superior rewards that their ability and opportunity have provided for them? What more could they have accomplished if they had a “psychological worm” eating inside them—whether that worm was low self-concept or a need to prove something to someone or to the world—that would have driven these people to greater efforts. What if their aptitudes had been challenged in a more hard-driving manner, like Wiener’s experience, into the development of a specific talent? This book raises many important, sometimes disturbing issues… The authors raise some disturbing issues regarding the purposes of schools for the gifted. Indeed, just what is the contemporary rationale for funding schools or programs for the highly gifted student? If one is looking to such an institution as a source of leading students towards societal leadership (or, as the authors suggest, “a path to eminence”), then the Hunter College Elementary School of the past failed to realize such an aspiration. Indeed, this goal may well be beyond the reach of any elementary school…the [Hunter College] High School seeks to enhance students’ commitment to intellectual rigor and growth, develop opportunities for specialization, and commitment to caring and compassion. Will such a rationale foster more students down the path towards genius? The research literature and the current study would indicate that such a condition is a necessary but not sufficient condition to move students into making ground-breaking discoveries or toward professional eminence. Does it follow then that such schools should not exist? Or at least, not at public expense? I would vigorously argue against both reactions.

This appraisal of failure has been echoed by people citing Genius Revisited like Malcolm Gladwell.⁴

This fits with the general description of the Hunter Elementary cohort on pg3–4:

The mean IQ of the Hunter sample was 157, or approximately 3.5 standard deviations above the mean, with a range of 122 to 196 on the L-M form.

…Each class at Hunter College Elementary School from the years 1948_76ya to 1960_64ya contained about 50 students, yielding a total possible population of 600 graduates…35% of the total population of 1948^–₁₂1960_64ya HCES students (n = 210) completed and returned study questionnaires

…Religious Affiliation: The Hunter group is approximately 62% Jewish, although they describe themselves as Jews more in terms of ethnic identity than religious practice. The group, as a whole, is not religious.

Educational Attainments: Over 80% of the study participants held at least a Master’s degree. Furthermore, 40% of the women and 68% of the men held either a Ph.D, LL.B., J.D., or M.D. degree.

Occupation and Income: Only 2 of the HCES women identified themselves primarily as homemakers. 53% were professionals, working as a teacher at the college or pre-college level, writer (journalist, author, editor), or psychologist. The same proportion of HCES men were professionals, serving as lawyers, medical doctors, or college teachers. The median income for men in 1988_36ya was $204,183.07^$75,000₁₉₈₈ (range = $1,361,220.48^$500,000₁₉₈₈) and for women $108,897.64^$40,000₁₉₈₈ (range = $460,092.52^$169,000₁₉₈₈). Income levels were statistically-significantly different for men and women, even when matched by profession. For example, the median income for male college teachers or psychologists was $136,122.05^$50,000₁₉₈₈ and for females, $81,673.23^$30,000₁₉₈₈.

By regular standards, this is a remarkably high degree of accomplishment. Even now, only a small fraction of the population can be said to hold a “Ph.D, LL.B., J.D., or M.D.”, but in the Hunter Elementary cohort, you could hardly throw a rock without hitting a professor (16% of men), who would then be able to turn to the person standing next to them to have their wound treated (18% doctors), and turn to the person on the other side in order to sue you for assault (20% lawyers). For this cohort, the education baseline would be more like <7%, not >80%. Subotnik et al 1989_35ya breaks it down a little more precisely in Table 2 “Highest Degree Attained”: for men, 4% not available, 20% Bachelors, 43% Masters, 40% Ph.D/L.L.B./J.D./M.D. The income levels are also sky-high: in 1988_36ya, median household income would’ve been ~$136,122.05^$50,000₁₉₈₈, and the ranges like $1,361,220.48^$500,000₁₉₈₈ indicate that Hunter Elementary incomes stem from life choices and career preferences as much as any limits from ability.

But it doesn’t fit the definition of great accomplishments. They mention no one winning a Nobel, or a Pulitzer, or being globally famous. Thus, in a real sense, Hunter Elementary has failed, and with it (the authors imply), the idea that IQ is the driving force behind greatness; thus, Subotnik et al spend much of the book, and other publications, pondering what is missing. If IQ is merely a necessary factor or threshold, but one that still leaves such a high chance of an ordinary life, what really makes the difference? Is the crucial ingredient a drive for mastery? Did Hunter Elementary accidentally quash students’ ambitions for a lifetime by de-emphasizing competition and grades? Or (as the other half of surveyed students maintained), did it have too much competition and broke the students mentally? Was Hunter Elementary too well-equipped a cocoon, leaving students unprepared for Hunter High and the real world, or not enough? Did the home environment determine this, or the curriculum? Did the broad academic curriculum leave students ‘a mile wide and an inch deep’ and lacking in fundamentals acquired by drilling and repetition?

Sample Size

But should we declare it a failure, considering the parallel lines of evidence from Roe, SMPY, and TIP? The mentioned standard is a high bar indeed. What percentage of the population can be truly said to ‘revolutionize a field’? It’s a lifetime’s work just to truly understand a field and reach the research frontier and make a meaningful contribution, and most of the population generally doesn’t even try but pursue other goals. Out of 600 students, is it reasonable to consider the Hunter Elementary experiment a failure because none has (yet—the Nobel Prize is increasingly delayed by decades)? As Gallagher then points out:

…Yet, there are very few such individuals alive in any particular era. The statistical odds against any one of them having graduated from one elementary school in New York City is great. Whether the “creative rebel” would have survived the selection process at Hunter, or any similar school, is one of those remaining questions that should puzzle and intrigue us.

If we consider the STEM Nobel Prizes, the USA has perhaps 1 per million people. So if even 1 HCES student had won a STEM Nobel out of 210, or 600, that would imply an enormous increase in odds ratio of >1666_358ya; or to put it another way, if we genuinely expected 1 or more Nobels from our HCES alumni, then to achieve that >1666_358ya increases in odds with only +57 early-childhood IQ points, we’d also have to believe something along the lines of each individual IQ point on average increasing the odds by 29 effect sizes, we would still frequently expect to observe a HCES-sized cohort to not win a Nobel (eg. if we had expected 1 Nobel prize per 600, for a probability of 1⁄600 per student, then the probability of seeing 0 Nobels in n = 600 is high: (1 − 1⁄600)⁶⁰⁰ = 0.367; to drive the non-Nobel probability down to <5%, we would have to expect ≥3 Nobels per 600).

One is reminded of the oft-head criticism of the Terman study for failing to enroll William Shockley & Luis Alvarez, the former of whose known IQ test scores as an 8–9yo fell short by ~11 points of the nominal threshold (or 6 points for special-cases Terman might admit): a sample of hardly 1500_524ya children, whose selection was inevitably imperfect⁵, particularly when pioneering longitudinal studies, is supposed to contain all the Nobelists from a population at least 100 times the size (the screening population was nominally >168,000 Californian children), or else this debunks IQ somehow. What method of selection could accomplish this feat is never specified, nor do critics concede that it is impressive that IQ tests could come so close to picking out the children in elementary school who had a chance of many decades later becoming Nobelists despite all the limitations the Terman study labored under (like using a verbal-heavy IQ test). From a purely statistical perspective, given what is known about the instability of childhood test scores and regression to the mean and the relatively small Terman sample combined with the extreme rarity of Nobel prizes and randomness, the Terman study would be expected to miss at least one future Nobelist the majority of the time (Warne et al 2019).

So it’s unclear how much weight we ought to put on the apparent ‘failure’ of the HCES alumni, because even the ludicrously optimistic model is consistent with often seeing ‘failure’.

Alumni

How many people from Hunter Elementary and from Hunter High come anywhere close to being nationally famous?

If we were to double-check in Wikipedia by looking for ‘Notable’ people whose entries link to Hunter Elementary, perhaps because they were students there, we find painter Margaret Lefranc, linguist E. Adelaide Hahn, and minor actor Fred Melamed, and Supreme Court justice Elena Kagan (but while her mother taught at Hunter Elementary, she herself went to Hunter College High School—along with at least 95 other ‘Notable’ people). I later learned that Hamilton star Lin-Manuel Miranda and scientist Adam Cohen also went to Hunter Elementary as well as High.

Triple-checking in Google, this does seem to be a fair accounting—no billionaires or Nobelists suddenly pop out. If we were to judge by Wikipedia entries, it would seem that Hunter Elementary can claim around 5 ‘Notable’ alumni while Hunter High can claim 96. (Checking the 96 WP entries by hand, most omit mention of the elementary school or whether they passed exams to get into Hunter High, but the ones who do always specify exams or a non-Hunter Elementary; only 1 entry, the group entry for the hip-hop band Dujeous, turns out to include a Hunter Elementary member: Loren Hammonds/“Mojo the Cinematic”. Overall, this comparison may be somewhat biased against Hunter Elementary but I don’t think hugely so.)

This is not because Hunter High is 32× larger than Hunter Elementary: Hunter Elementary currently accepts ~50 students per year while Hunter High currently accepts ~175 + 50 grandfathered in from Hunter Elementary (total ~225), and is only 4.5× bigger—3.5× if we exclude the Hunter Elementary alums (who do not appear in the 95+ listed, apparently). Even more strikingly, while I do not recognize the names of Lefranc, Hahn, Melamed, or Adam Cohen, I do recognize several names on the Hunter High list (Kagan, of course, but also Bruce Schneier, Mark Jason Dominus, some rappers in passing).

This would imply that Hunter High grads are much more likely to achieve WP ‘Notability’ than Hunter Elementary grads: something like 8 times more likely. It is also worth noting that some other selective urban schools pass the ‘Nobel test’: Lowell High School in SF, for example, boasts 3 Nobel laureate alumni (Michelson, Erlanger, & Cornell); Stuyvesant High School claims (Lederberg, Fogel, Hoffmann, & Axel).

Why?

Another way would be to ask what should we expect, from a statistical and psychometric point of view, from Hunter Elementary students, given the procedures and tests used? There are a number of statistical issues which can arise in intelligence research particularly: range restriction such as ceiling/floor effects, measurement error biasing correlations down and requiring correction, sampling error, loss of measurement invariance in IQ tests or test-specific learning leading to hollow gains (particularly prevalent in interventions), genetic confounding of correlations between IQ and other variables like SES, test-retest reliability, mistaken “controlling” for intermediate variables (like “controlling for education” and then claiming IQ has no causal effect), and so on. (Many of these are discussed in more detail in Hunter & Schmidt’s 2004_20ya textbook Methods of Meta-analysis: Correcting Error & Bias in Research Findings.) As Hunter Elementary used and still uses a legitimate IQ test (Stanford-Binet Intelligence Scales), the results are not interventional or claimed to be causal, and we are concerned with them as a group compared to the general population, the last issue of reliability/predictive validity is the one which bothers me the most in trying to interpret the results.

Weak Childhood IQ Scores: Regression To The Mean

Regression to the mean is pervasive: individual data points which are “unusual” in some way will tend to be associated with more “usual” data points. If you run unusually fast one day, you will probably run slower than that the next day—or the day before; if you weigh unusually little on your bathroom weight scale one morning, and you immediately weigh yourself again, you will probably ‘gain weight’ to a more usual weight; while if a relative is unusually morbidly obese, you are more likely to be overweight, but not as overweight as them. So, unusually successful parents will tend to have more usually (ie. less) successful children; and also unusually successful children will tend to become more usually successful adults. This is true of every trait, whether height or IQ.

Hunter Elementary uses IQ testing of ~5yo children, selecting those >IQ 140 and getting a mean of IQ 157 (3.8 SDs); these children are then kept enrolled in Hunter Elementary and grandfathered into Hunter High as long as their grades stay reasonable, with expulsions and transfers apparently rare (and little mentioned in the book). This is fine as far as the 5yo children go… but what about them as adults?

As is well known, childhood IQs are imperfect predictors of final adult IQs, for neurological, developmental, and genetic reasons; the best possible measurement at 5yo will only correlate with adult IQ at perhaps r = 0.5–0.6. (Reliabilities/test-retest correlations/between-test correlations have been reported extensively in the psychometric literature, eg. Månsson et al 2018, or TEDS, or Trucker-Drob & Briley2014/Breit et al 2024 and the increasing stability of IQ test scores with age—and the regression to the mean of the highest-scoring children—has been noted since at least Thorndike1940, who cited previous reviews, Foran 1926_98ya/Foran1929/Nemzek1933; an obscure but interesting dataset in this respect is the Fullerton Longitudinal Study which has intensive testing age 1–17, showing eg. a r = 0.60 of age 5/age 17.)

Such a correlation is considerable, and similar to the correlation of years of education & IQ, but it is also far from the r = 1 implicitly assumed by Subotnik et al when they casually talk of their students as adults having IQ 150+ simply because, long ago, as small children, they had nominal test scores that high.

Such a correlation implies that the childhood IQ test scores are being driven by, as much as their ultimate intelligence, factors like precocity, patience for testing and conformity, and simple randomness⁶; by selecting this early, one is selecting less for extremely intelligent adults than for cognitively fast-developing children, which is not the same thing.

And having been selected for scoring extremely high on a particular test, Hunter Elementary kids must revert to mediocrity (a phenomenon described by Galton well before any IQ test was developed, and which all psychometricians are mindful of, especially in any kind of test-based selection process).

What can we estimate their adult IQs to be? Since the majority of students are Jewish (or these days, split between those of Jewish and East Asian descent) whose mean is usually estimated at something like 110, we could predict that their adult IQs will not average 157, but will average 110 + (157 − 110) × 0.5 = 133. (Note that if we do not grant this assumption, the regression to the mean would be more severe: 100 + (157 − 100) × 0.5 = 128.)

133 IQ is nothing to sneeze at, but it is also only +2.2SDs and closer to 1 in 50 than 1-in-10,000; a Hunter Elementary school grad as an adult could easily not even qualify for Mensa. Or to put it another way, with 260 million people in the USA in 1993_31ya, there were around 3.6 million people with IQs ≥133, of which the total Hunter Elementary cohort would represent 0.016%. If we consider cohorts of 600 children with adult mean IQs of 133, not many of them will be >157 at all—only 5% or ~32 students (mean(replicate(100000, sum(sort(rnorm(600, mean=133, sd=15))>157))))! The others will have developed into adult IQs below that, possibly much below that. This calculation doesn’t require any knowledge of outcomes and could have been done before Hunter Elementary opened: inherently, due to the limits of IQ tests in screening for extremely gifted adults based on noisy early childhood tests, most ‘positives’ will be false positives. (This is the same as the famous mammography or terrorist screening examples of how an accurate test + low base-rate = surprisingly high false positive rate and low posterior probability.)

Subotnik et al appear entirely ignorant of this, particularly in chapter 9, as they repeatedly state or quote former Hunter students echoing estimates like “160 IQ”, at face-value, and are puzzled at the failure of HCES students to attain the pinnacles of global success and ponder whether HCES damaged them by fostering mediocrity & crushing ambition, which is to reach for explanations for something which requires no explanation. (This is particularly ironic given that they contrast the ‘failure’ of HCES with the success of other institutions, such as the Illinois University High School.)

Implications for Gifted Education

Given this, we would have to conclude that the idea of a gifted & talented elementary school is difficult to justify on the resource paradigm related to focusing resources on students’ with future adult intelligence >150 as only a small fraction of such students are findable with current IQ testing methods at that age, but that it makes far more sense to screen at a later age like 11yo and concentrate resources at high school or college levels. If we concluded that the gain from better education of those 5% in an elementary school is profitable and so a Hunter-like elementary school is a good idea, we should definitely not automatically enroll all such elementary school students in an even more expensive Hunter-like high school: each such grandfathered student is worth ~1⁄8^th an outsider student in terms of potential. It would be much better to not grandfather the elementary school students—they have already been highly advantaged by the enriched education & peers, after all, so why should they be given an additional huge advantage over all the students outside the system who are equally deserving of the chance? The main reason would seem to be some sort of ‘family’ or loyalty sentimental reasoning; if this bias cannot be overcome, the idea of a single vertically integrated feeder system may be actively harmful to gifted education.

Improving HCES?

Matters could be improved, though, with more broad-ranging tests.

For example, genetics: as adult IQ is a highly heritable trait with perhaps up to 80% of variance predictable from all genetic variants and >~50% predictable from all SNPs, with the heritability increasing with age and only ~25% at age 5 (the Wilson effect, Bouchard2013), predictions of adult IQ based on 5yo testing could be improved substantially using their parents’ & siblings’ IQs, or by direct genetic prediction; this would help identify the children who are rejected because of developmental quirks but who would eventually live up to their genetic potential.

If we consider a path model with genes → IQ (0.50), IQ_5yo → IQ (0.50), genes → IQ_5yo (0.25):

model <- 'IQ_adult ~ 0.8*Gene + 0.5*IQ_5
          IQ_5 ~ 0.25*Gene'
d <- simulateData(model)
s <- sem(model, std.ov=TRUE, data=d)
semPaths(s, "Standardized", "Estimates", style="lisrel", curve=0.8, nCharNodes=0,
    edge.color="black", label.scale=FALSE, residuals=FALSE, fixedStyle=1, freeStyle=1,
    exoVar=FALSE, sizeMan=10, sizeLat=24, label.cex=3, edge.label.cex = 2.2)

Then using an ideal SNP genetic score and a 5yo IQ test, one could expect to predict 0.5 + (1 − 0.25) × 0.5 = 0.875 or 87% of variance, giving a prediction/adult IQ of √0.875 = 0.93; with this sort of predictive power, the regression to mediocrity is minimal and Hunter Elementary kids would then have adult IQs of 110 + (157 − 110) × 0.93 = 153.

In that scenario, we could create a Hunter-like Elementary school which is as good at filtering as Hunter High is. While it’s unclear when we will be able to predict 50% of variance in adult IQs based on polygenic scores, in the near future we can hope for polygenic scores on the order of 10%, which would still be helpful: PGS = 0.10; 110 + (157 − 110) × √(PGS + (1 − 0.25) × 0.5) = 142.4. Besides waiting for better polygenic scores, other factors could be included in a predictive model such as parental IQs and income/education, sibling IQs, and race. I don’t know if such an elementary school for the gifted would be feasible, however: more accurate predictions will increase the existing controversial racial disparities which make the NYC magnet elementary & high schools a lightning rod for liberal activism, the selection may strike the public as even more ‘unfair’ than it is now (which it will be as it even more accurately picks up existing group differences rather than benefiting lower-mean groups through measurement error), and will inherently yield classrooms with more cognitive inequality at the moment which may itself impede the educational mission or foster resentment & rivalry.

Ultimately, it would seem that the most justifiable reason for running Hunter Elementary is the reason that comes across most clearly reading the alumni reminiscences: because they would have been miserable in regular schools. If early-developing children must be subjected to mandatory formal education, then it should at least be with their peers.